A note on the singular Sturm-Liouville problem with infinitely many solutions

Abstract

We consider the Sturm-Liouville nonlinear boundary-value problem $$ displaylines{ -u''(t) = a(t)f(u(t)), quad 0 0$ and $a(t)$ is in a class of singular functions. Using a fixed point theorem we show that under certain growth conditions imposed on $f(u)$ the problem admits infinitely many solutions. Submitted November 13, 2001. Published September 27, 2002. Math Subject Classifications: 34B16, 34B18. Key Words: Sturm-Liouville problem; Green's function; fixed point theorem; Holder's inequality; multiple solutions.

Keywords

• Sturm-Liouville problem
• Green's function
• fixed point theorem
• Holder's inequality
• multiple solutions.